1. Technical Field
This invention relates generally to a system and method for efficient upsampling and filtering, and more specifically to a system and method for upsampling and filtering without the use of a low-pass filter.
2. Background Art
Digital audio systems rely upon analog to digital converters for their operation. Analog to digital converters allow a conventional analog waveform, like acoustic energy for example, to be sampled and quantized into a data stream of binary numbers. The conversion from an analog waveform to digital number sequence allows computers and microprocessors to accurately and reliably store, recall, transform and reproduce audio sound.
During this sampling process, the analog wave is effectively “chopped up” into discrete digital values. The sampling process, by its very nature, introduces quantization noise into the analog to digital system, as the formerly smooth analog wave essentially becomes a piece-wise linear approximation of that wave. In addition to the quantization noise, a phenomenon known as “aliasing” causes multiples of the analog wave to appear as duplicate images above the frequency of interest. These duplicates will compromise the quality of signal when the discrete digital values are converted back into an analog wave.
For example, an audio signal having frequency components ranging from 0 to 22 kHz must be sampled, in accordance with Nyquist's Theorem, at a frequency of at least 44 kHz. In addition to quantization noise, duplicate images will appear at multiples of the original analog frequencies. A first duplicate appears from 22 kHz to 44 kHz, a second duplicate appears at 44 kHz to 66 kHz, and so forth.
To eliminate quantization and oversampling noise, prior art systems employed very high-order, complex low-pass filters to eliminate frequency components above the desired frequency. Using the example in the preceding paragraph, a designer may employ a fourth or fifth order Chebychev filter to try and eliminate all frequency components above 22 kHz. The problem with these filters is not only are they expensive, but they often became unstable and introduce other forms of noise into the system.
To rectify these problems, designers have begun using a process known as oversampling. In oversampling, rather than sampling the analog signal at twice the maximum frequency of interest, the system may sample the analog signal at four, eight or even sixteen times the maximum frequency of interest. Continuing with the example from above, the 0–22 kHz signal may be sampled at 88 kHz, 176 kHz or 352 kHz. This oversampling causes the duplicate images to be pushed to higher and higher frequencies. For example, at 4× oversampling, the first image appears at 66–88 kHz, rather than 22–44 kHz. Additionally, as the oversampling rate increases, the quantization noise becomes spread across a larger spectrum, thereby increasing the signal to noise ratio. As a result, simpler, lower-order low-pass filters may be used to eliminate the duplicates.
Designers also realized that a similar process, upsampling, could be carried out in the digital domain to increase the overall quality of the signal. The process of upsampling is similar to oversampling, in that a digital data stream of one frequency is increased to a higher frequency. In upsampling, the process is carried out by inserting additional samples between the initial samples. These additional samples may be either zeroes or interpolated values between adjoining data points.
As with oversampling, in conventional upsampling systems an upsampled data stream is passed through a low-pass filter to remove any duplicate images introduced by the upsampling process. The filtered, upsampled data stream may then be passed on to other signal processing modules, circuits and components.
The problem with these prior art upsampling systems is that the low-pass digital filter requires both time and processing power when in operation. This time and processing power, especially in the realm of battery-powered, mobile electronics, can come at the expense of other functions. Additionally, the processing power required to implement these filters is “multiply and accumulate” processing power. In the world of microprocessors, performance is sometimes determined by how many multiply and accumulate (MAC) operations the processor can perform in one second. As there is a finite amount of MAC operations that a device may perform, for every one that must be dedicated to filtering, one less is available for other functions.
There is thus a need for an improved upsampling system with increased efficiency.
Skilled artisans will appreciate that elements in the figures are illustrated for simplicity and clarity and have not necessarily been drawn to scale. For example, the dimensions of some of the elements in the figures may be exaggerated relative to other elements to help to improve understanding of embodiments of the present invention.